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| Lindstrum A.O. — Abstract algebra |
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| Предметный указатель |
 103
 110
Abelian group 57
Absolute value of integers 36
Addition of natural numbers 9
Additive exponent 20
Additive group of N 17
Adjacent words 70
Adjunction 138
Algebra 112
Algebra of rational quaternions 115
Algebra, linear associative 112
Algebra, linear nonassociative 112
Algebra, polynomial 117
Algebra, total matric 169
Algebraic element 135
Algebraic field 136
Algebraic systems 100
Algebraic systems, product of 100
Algorithm, division 118
Alternating group 81
Antecedent of a natural number 9
Anti-automorphism 78
Anti-isomorphism 78
Associate 38
Associative algebra 112
Associative law 7
Associative law for mappings 18
Associative law generalized 19
Automorphism inner, of a group 29
Automorphism of a semigroup 29
Automorphism of algebraic systems 101
Automorphism outer, of a group 59
Basis of an Abelian group 94
Basis of an R-module 108
Belongs to 2
Bilateral ideal 128
Binary operation 6
Cancellation law 10
Canonical matrix, classical 198
Canonical matrix, Jordan 196
Cartesian product 5
Cauchy 75
Cayley 79 202
Center of a group 61
Central of a group 61
Characteristic of a field 93 99 143
Characteristic of a ring 93 99
Characteristic polynomial 202
Circular permutation 79
Classical canonical matrix 199
Closed 6 97
Coefficients leading 117
Coefficients of a linear combination 105
Coefficients of a polynomial 117 127
column see "property without the modifier column"
Common part 3
Commutative group 57
Commutative property 6 7
Commutative ring 95
Companion matrix 196
Compatible 13
Compatible with the structure of a ring 130
Complete set of conjugates 63
Complete set of residue classes modulo m 43
Component 66 103
Composite 6
Composite of a finite sequence of elements 19
Composition external 97
Composition internal 5
Composition series 90
Composition, factors of 90
Composition, table of a semigroup 28
Congruence modulo m 43
Conjugate elements of a group 63
Conjugate elements over a field 145
Conjugate quaternions 115
Conjugate subfields 142
Conjugate subgroups 63
Contained in 2
coordinates 173
Cosets of a group 53
CYCLE 79
Cyclic group 47 73
Cyclic linear transformation 195
Cyclic permutation 79
Cyclic space 193
Cyclic subgroup 49
Cyclotomic extension of a field 153
Cyclotomic field 152
Cyclotomic polynomial 153
Defined everywhere 6
Defining relations 73
Degree of a permutation 78
Degree of a polynomial 117
Degree of an element over a field 136
Degree of one field over another 136
Degree proper 185
Degree reduced 149
Derivative of a polynomial 121
Diagonal matrix 183
Difference ring 131
Dihedral group 62 73
DIMENSION 109
Direct product of groups 66
Direct sum of groups 66
Direct sum of R-modules 104 188
Direct sum of two linear transformation 188
Disjoint cycles 79
Disjoint sets 3
Distributive law 8
Division algorithm 118
Division ring 95
Divisor 37
Divisor elementary 201
Divisor greatest common 38
Divisor of zero 94
Divisor proper 38
Divisorless ideal 131
Domain integral 95
Domain of integrity 95
Eisenstein's theorem 124
Element adjacent 70
Element conjuate, of a group 63
Element conjugate, over a field 145
Element identity 93
Element inseparable 148
Element neutral 22
Element period of 50
Element permutable 95
Element primitive 154
Element primitive, theorem 155
Element regular 94
Element separable 148
Elementary divisor 201
Elementary matrix 177
Elementary operations on a matrix 176
Empty set 3
Empty word 70
Endomorphism of a semigroup 29
Endomorphism of an algebraic system 100
Endomorphism, sum of 89
Equality 2
Equality of mappings 4
equation see "polynomial"
Equation homogeneous 175
Equation nonhomogeneous 175
Equation pure 160
Equivalence class 26
Equivalence of matrices 176 177
| Equivalence relation 26
Essentially unique factorization 41
Euclidean Domain 125
Euler 43 45
Euler totient function 45
Even integers 45
Even permutation 87
Everywhere defined 6
EXPONENT 20 37
Exponent additive 20
Exponent multiplicative 20
Extension algebraic 136
Extension cyclotomic 158
Extension Galois 156
Extension of a mapping 5
Extension of a semigroup 31
Extension pure 160
Extension transcendental 136
External composition 97
F-automorphism 141
F-isomorphism 144
Factor group 57
Factor invariant 201
Factor of composition 90
Factor, prime factor group 90
Factorization, unique 41 42 123
Factors completely 139
Fermat 45
Field 95 153
Field cyclotomic 152
Field finite 153
Field Galois 153
Field inseparable 148
Field normal 146
Field of quotients 97
Field of quotients of polynomials 127
Field of ratvional numbers 97
Field prime 143
Field root 140
Field separable 148
Field splitting 140
Field stem 139
Finite characteristic 94
Finite extension 133
Finite group 23
Finite sequence 19
For each, for every, for all 1
Form, Smith normal 184 196
free 107
Free group 71
Free module 108
Function, polynomial 120
Galois extension 156
Galois field 153
Galois group 157
Galois resolvent 156
Galois theory of fields 156
Gauss' lemma 124
Gaussian semigroup 123
Generator of a group or semigroup 49
Greatest common divisor 38
Group 23 24
Group alternating 81
Group cyclic 49
Group factor 57
Group free 71
Group Galois 157
Group generators 49
Group product 27
Group quotient 57
Group simple 77
Group subgroup 24
Group symmetric 78
Group with operators 98
Hamilton 202
Hoelder 92
Homogeneous equations 175
Homologous 100
Homomorphism of algebraic systems 101
Homomorphism of semigroups 29
Ideal 128
Ideal bilateral 128
Ideal divisorless 131
Ideal maximal 131
Ideal prime 131
Ideal principal 129
Ideal principal, ring 129
Ideal two-sided 128
Identity element 93
Identity mapping 4
Image 3 5
Imbedding of a semigroup 31 33
IMPLY 1
Improper subgroup 46
Indeterminates 117 127
Indexing set 5
Induced law in quotient set 3 1
Induced law in subset 21
Induction, mathematical 9
Inequality of natural numbers 14
Inner automorphism 59
Inseparable element 148
Inseparable field 148
Inseparable polynomial 148
Integers 35
Integers absolute value of 36
Integers negative 36
Integers positive 36
Integral domain 95
Integrity, domain of 95
Internal composition 5
Intersection 3
Invariant element 98
Invariant factor 201
Invariant maximal subgroup 89
Invariant subgroup 56
Invariant subspace 187
Invariants of an Abelian group 84
Invariants, similarity 201
Inverse element 22
Irreducible element 38
Isomorphism of algebraic systems 101
Isomorphism of semigroups 29
JORDAN 90
Jordan canonical matrix 196
Kernel 57
Lagrange 54
Law associative 7 19
Law cancellation 10
Law commutative 7
Law distributive 8
Law induced in quotient set 31
Law induced in subset 21
Law of external composition 97
Law of internal composition 5
Law of trichotomy 11
Leading coefficient 117
Least common multiple 38
Least residues modulo m 43
Left see "property without adjective left"
Length of a word 70
linear combination 105
Linear dependence 105 107
Linear mapping 165
Linear mapping, matrix of 169
Linear transformation 165
Linear transformation nonderogatory 195
Linear transformation nonsingular 165
Linear transformation relation 111
Logic 1
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